Buy some middle priced low output pickup like GFS, put it in the bridge and throw your neck pickup away(it'll change nothing but any guitar with empty pickup slot looks kickass). Or do it vice versa, put new pickup in the neck and throw away the bridge pickup, it'll give warmer tone.

Ice-picking pickups are common problem for majority of budget guitars. Cheap ceramic magnets(usually) and hot winding are the reasons. Throwing away your pot just increased the whole effect. My Squier Bullet Strat is ice-picking as hell, though I play it mostly unplugged_________________